Question: $4tu - 3tv - t + 8 = -7u + 9$ Solve for $t$.
Answer: Combine constant terms on the right. $4tu - 3tv - t + {8} = -7u + {9}$ $4tu - 3tv - t = -7u + {1}$ Notice that all the terms on the left-hand side of the equation have $t$ in them. $4{t}u - 3{t}v - 1{t} = -7u + 1$ Factor out the $t$ ${t} \cdot \left( 4u - 3v - 1 \right) = -7u + 1$ Isolate the $t$ $t \cdot \left( {4u - 3v - 1} \right) = -7u + 1$ $t = \dfrac{ -7u + 1 }{ {4u - 3v - 1} }$ We can simplify this by multiplying the top and bottom by $-1$. $t= \dfrac{7u - 1}{-4u + 3v + 1}$